During the starting of the combustion engine with direct injection a start and a after-start enrichment is undertaken in general, whereby a fuel amount is injected that is increased compared to a normal operation. The reason for that is that a wall film can evolve on a piston head and a cylinder wall during the starting process in the combustion chamber, so that a lower fuel mass is available for the combustion. The wall film evolving is directly depending on a bad mixture formation, which can be caused by a too low pressure in a high pressure system of the injection system. Generally the described usual procedure has the disadvantage that a bigger fuel amount is required and that an unclean combustion is possible. Acquainted solution possibilities, as for example the heating of the fuel and the combustion engine before starting, are energy-intensive, time-consuming or disadvantageous in a different way.